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Modified asymptotic orders of the direct Filon method for a class of Volterra integral equations. (English) Zbl 1310.65170

Summary: The direct Filon method provides efficient approximation for solutions of Volterra integral equations with highly oscillatory kernels. In this paper, we study the rate of convergence of this method for a class of equations with trigonometric kernels. The asymptotic order is developed by examining the property of the solution. Numerical experiments are included to verify the given order.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45L05 Theoretical approximation of solutions to integral equations
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